Method of interior variations and existence of S-compact sets

Abstract

The variation of equilibrium energy is analyzed for three different functionals that naturally arise in solving a number of problems in the theory of constructive rational approximation of multivalued analytic functions. The variational approach is based on the relationship between the variation of the equilibrium energy and the equilibrium measure. In all three cases the following result is obtained: for the energy functional and the class of admissible compact sets corresponding to the problem, the arising stationary compact set is fully characterized by a certain symmetry property.